The main theme of this thesis could be classified into three objectives. These are summarized as follows: The first objective is to study nonlinear integral equations, as well as its classification. The most important difficulty of the subject of nonlinear integral equations is the existence and uniqueness of the solution of them. The second objective is to study the variational formulation of every nonlinear operator, which has its basis on Tonti's approach, with some simplifications and some illustrative examples. The third objective of this thesis is the application of Tonti's approach to nonlinear integral equations. This application has its difficulty in satisfying the so many conditions of Tonti's approach to nonlinear integral equations. In this work, we give a full description of this approach, which is illustrated with some numerical examples.